... the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and super harmonics in the response. The broadband structure of the frequency spectrum, the fractal structure of the Poincare maps, and the bifurcation diagram as qualitative...

... surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components...

... and Information in Engineering Conference , Las Vegas, NV, Sept. 4–7, pp. 1335 – 1338 . 07 09 2009 01 03 2011 12 04 2011 12 04 2011 chaos nonlinear dynamical systems Poincare mapping time series chaotic vibration time series vibration system phase space reconstruction...

..., chaotic motion, n T solutions, etc., are identified with the help of phase plots and Poincaré map sections. Frequency response diagram: ( a ) from a frequency of 0.05 rad/s to 0.5 rad/s (in expanded horizontal scale); ( b ) from a frequency of 0.5 rad/s to 2 rad/s (in reduced vertical scale...

... of the eigenvalues of the linearization of a suitably defined Poincaré mapping, indicating the destabilizing influence of near-grazing contact. di Bernardo , M. , Budd , C. J. , and Champneys , A. R. , 2001 , “ Normal Form Maps for Grazing Bifurcations in n-Dimensional Piecewise-Smooth Dynamical...

..., and the complex behaviors of the nonlinear dynamical system are simulated numerically, including the trajectory of the journal and phase portrait. In particular, the stabilities of the system’s equilibrium position and unbalance responses are studied via the orbit diagram, phase space, Poincaré mapping...

... cutting, and it is possible to analyze continuous and intermittent cutting as stationary and nonstationary processes, respectively. The influence of the axial and torsional dynamics of the tool on chip formation is considered. The Poincaré maps of state variables for various sets of operating conditions...

... in such a Hamiltonian system are presented through the incremental energy approach. The Poincaré mapping surfaces of chaotic motions for this specific nonlinear Hamiltonian system are illustrated. The chaotic and quasi-periodic motions on the phase planes, displacement subspace (or potential domains), and the velocity...